Call a positive integer n "favorable" if there is a set of n distinct positive integers whose reciprocals' sum adds to 1.

How many unfavorable numbers are there?

Just have to agree with the others:

1 = 1/1
1 = 1/2                      + 1/3  + 1/6
1 = 1/2 + 1/4                + 1/6  + 1/12
1 = 1/2 + 1/4 + 1/8          + 1/12 + 1/24
1 = 1/2 + 1/4 + 1/8 + 1/16   + 1/24 + 1/48

etc. etc. etc.

But the real question is: If n is favorable, how many different sums in its favor exist?

Posted by JLo on 2006-11-02 13:42:05